In general, it’s not believed that Sandor Clegane is dead, despite the testimony of Elder Brother and others. The reason for this is quite simple: the gravedigger.

When Brienne visits the Quiet Isle, she notes that the novices of the order are not only sworn to silence, but wear woolen scarves that hide their faces. While walking up the path to see Elder Brother, she notices a novice digging in the lichyard who’s described as even larger than her and lame (IV: 463). When Dog goes up to him, he drops his spade and scratches the dog’s ear (IV: 464). Later, during a meal, the novice is described moving with a half-lurching gait (IV: 467). Finally, when Brienne discusses Sandor Clegane with the Elder Brother, she dejectedly remarks that Sandor Clegane is dead, to which he responds, "He is at rest." (IV: 470) Later, he says, "the Hound is Dead".

GRRM has previously stated that Sandor Clegane is taller than Brienne (SSM). As last seen in ASoS, he had taken a wound to his hip that became dangerously infected, recovery from which could very likely leave his movement in that leg impaired. And as he told Sansa in ACoK, he was fond of dogs (II: 211). These details all fit the large, limping, dog-loving novice. Combined with Elder Brother’s very specific phrasing—that Sandor Clegane is "at rest" but that "the Hound" is dead—it’s been understood that Elder Brother is hiding the truth without outright lying. The novice who is trying to find peace on the Quiet Isle is Sandor, who has put aside the rage and hatred that made him the Hound, "killing" that part of his persona.